Unit 5 - Trigonometry | Multiple Angles

Multiple Angles is the first chapter in Trigonometry for Class 10 students who are studying Optional Mathematics subject.

Any angle that can be expressed as a greater multiple of a reference angle is said to be multiple angles.

For example: let the reference angle be A then 2A, 3A, 4A, ... are said to be the multiple angles of A.

As always, we will have some major formulae in this chapter as well. We have to remember the formulae to express sin, cos, tan and cot in terms of multiple angles of 2A and 3A.

All exercises of Trigonometry Class 10:

Exercise 1

3. Prove the following identities:

a)  

b)  

c)  

d)  

e)  

f)  


4. Prove that:

a) $\dfrac{1 - sin2A}{cos2A} = sec2A - tan2A$

b) $\dfrac{cos2A}{1 + sin2A} = \dfrac{1- tanA}{1 + tanA}$

c) $\dfrac{1 + cos2A}{sin2A} = cotA$ Answer

d)

e)

f)

g)

h)

i) (1 +sin2A -cos2A)\(1 +sin2A +cos2A) = tanA

j)

k) 1 + tan4A.tan2A = sec 4A Answer

l)

m) $\frac{sin4A}{sin2A} × \frac{1 - cos2A}{1 - cos4A} = tanA$ Answer

n)

o) Answer

p)

r)



5. Show that:

d)

f)

h)


6. Prove the followings:

d)

f)

h) sin5A = 16 sin⁵A -20sin³A +5sinA

j)

l)

n) cos²A +sin²A.cos2B = cos²B +sin²B.cos2A

p) 1/(tan3A +tanA) -1/(cot3A+cotA) = cot4A



7 a) If tan A = x/y, prove that: y.cos2A + x.sin2A = y.


8 a) 


About Readmore Optional Mathematics Book 10

Author: D. R. Simkhada
Editor: I. R. Simkhada

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Class 10 - Multiple Angles - Trigonometry Solved Exercises || Readmore Optional Mathematics is a collection of the solutions related to multiple angles of Trigonometry for Nepal's Secondary Education Examination (SEE) appearing students.

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